Signal amplitude and phase homodyne

ABSTRACT

Homodyne signal detection apparatus which utilizes a unitary signal channel including a single mixer for processing an applied input signal with successively applied waveforms separated in phase by pi /2 radians is disclosed. The product signals of each waveform and the input signal are filtered, stored, and selectively combined to develop signals which are sinusoidal or cosinusoidal functions of the phase angle of the applied signal and have magnitudes proportional to the amplitude of the input signal.

United States Patent Maybach 1 1 May 23, 1972 54] SIGNAL AMPLITUDE ANDPHASE 3,286,176 11/1966 Bimboim ..328/l33 x HOMQDYNE 3,430,143 2/1969Walker et ....328/133 X 3,500,217 3/1970 Allen ....329/124 X [72]Inventor: Richard Lee Maybach, Holrndel, NJ. 3 5 274 2 197 Di 325/444 X[73] Assignee: Be Tekphone Laboramfies Incorporated 3,609,557 9/1971Goell ..325/444 X 11, NJ. Murray Primary Examiner-Smiley T. Krawc'zewlczFiled: 1 1970 Att0meyR. J. Guenther and William L. Keefauver 21 Appl.No.: 101,813 [57] ABSTRACT Homodyne signal detection apparatus whichutilizes a unitary [521 U.S. c1 53228748 53, 3 2 :6112, 33225471422signal channel including a Single mixer for processing an 5]] In rim")1/16 plied input signal with successively applied Wavefonns 58] Fieid325/444 separated in phase by 17/2 radians is disclosed. The product331/25 3287133 signals of each waveform and the input signal arefiltered, stored, and selectively combined to develop signals which aresinusoidal or cosinusoidal functions of the phase angle of the [56]Re'erences cued applied signal and have magnitudes proportional to theam- UNITED STATES PATENTS Pliwde of the input Signal- 2,964,622 12/1960Fire ..328/133 X 19 Claims, 3 Drawing Figures L Yo "'J -1 MIXER LPF GATEI 1 SIGNAL 39 I INPUT t A 35 43 1 33 Y AMPLITUDE I GATE STORE SUBTRACTQRm 23 Q2 35 44 (FIG.

GATE STORE SUBTRACTOR Z Q I P 7 32 31L .1

wNc. GEN, 27

COMPUTATION APPARATUS Patented May 23, 1972 3 Sheets-Sheet 5 I SIGNALAMPLITUDE AND PHASE I-IOMODYNE BACKGROUND OF THE INVENTION processingapplied signals with quadrature related modulating signals. The use oftwo mixers, and the requirement for precise analog phase shiftingapparatus gives rise to a number of problems. In practice, it has beenextremely difficult to maintain the exact quadrature relationshipbetween the two channels of the detector. Furthermore, each mixer gainmay vary and be affected differently by temperature and aging; also,additive d.c. (offset) terms, introduced in each channel, may vary withtemperature, time, and applied signal level. It is clear that each ofthese sources of error contributes to an unreliable measurement ofsignal amplitude and phase.

SUMMARY OF THE INVENTION In accordance with the principles of thisinvention, these limitations of prior art homodyne detectors areovercome by using a single, i.e., unitary, signal channel, including asingle mixer, for processing an applied input signal with successivelyapplied waveforms separated in phase by 7r/2 radians. The productsignals of each waveform and the input signal arefiltered, stored, andselectively combined to develop signals which are sinusoidal orcosinusoidal functions of the phase angle of the applied input signaland have magnitudes proportional to the amplitude of the input signal.

BRIEF DESCRIPTION OF THE DRAWING FIG. I is a block diagram of prior artsignal amplitude and phase measuring apparatus; 7

FIG. 2 is a block diagram of signal amplitude and phase measuringapparatus in accordance with this invention; and

FIG. 3 depicts various signal waveforms which are utilized in theapparatus of FIG. 2.

DETAILED DESCRIPTION OF THE INVENTION In the prior art homodynedetection apparatus of FIG. 1, a signal to be measured is applied toinput terminal 11 and conveyed to mixers, i.e., product modulators, 13and 14. A reference signal, of the same frequency as the input signal,is simultaneously applied to reference input terminal 12 and in turnapplied directly to mixer 14 and, via 1r/2 phase shift network 15, tomixer 13: The result product signals of mixers 13 and 14 are applied,respectively, to low-pass filters 16 and 17 to remove undesirable highfrequency signals. Thus, two signals, inphase and quadrature, eachproportional to the amplitude of the input signal and, respectively, asinusoidal or cosinusoidal function of the phase angle of the appliedinput signal, are, in theory, developed. In some applications, e.g.,making Nyquist plots, these two signals are satisfactory, but usuallythey must be converted to polar form. After the'two signals are squaredin devices 19 and 21, and combined by adder 22, a signal proportional tothe square of the amplitude of the input signal is, ideally, developed.Square rooter apparatus 20 develops a signal proportional to thesquareroot of the signal applied to it, and thus proportional to the amplitudeof the input signal, on output lead 23. Simultaneously, the signalsdeveloped by filters l6 and 17 are divided, one by the other, in divider24 to develop a signal proportional to thetangent of the phase angle ofthe applied input signal. This signal is processed by apparatus 25 todevelop the desired phase information on lead 26. The apparatus enclosedby broken line 18, i.e., squarers 19 and 21, adder 22, etc., will beidentified hereinafter as computation apparatus 18.

Assuming that the applied input signal may be designated as A cos (w t0), where w, is the radian frequency of the input signal and 0 itsphase, and assuming that the reference signal is equal to cos m t, theproduct signal of mixer 13 will be equal (0;

C A sin 0 D, G,A sin (2(1),: 0), (I) and the product signal of mixer 14will be equal to:

0 A cos 0+D +G A cos (2w,,!+0), (2)

where G and G are, respectively, the gains of mixers l3 and 14, and Band D are d.c. error or ofiset terms introduced by the mixers. v

After removal of the high frequency terms, the output of filter 16 isequal to:

G A sin 0+D (3) and the output of filter 17 is equal to:

G 14 cos 0+ D (4) It is clear that the presence of terms 6,, G and D,,D, adversely affects the proper computation of the amplitude and phaseof the input signal since squaring, adding, square rooting will notproduce a signal directly proportional to the amplitude A of the inputsignal, and dividing and processing by apparatus 25 will not produce asignal directly proportional to 6, the phase angle of the input signal.Of course, in the ideal case, mixer gains G and G are equal and thedrift terms D, and D are zero. Unfortunately, such is not the case inthe real world, and the conventional homodyne detector is inherentlyproductive of error. Furthermore, proper operation is absolutelydependent upon maintaining an exact quadratu're'relationship between thetwo modulating signals applied to mixers 13 and 14. As is well known, itis extremely difiicult to realize an analog phase shift network whichcomplies with this exacting criterion.

In accordance with the principles of this invention, these limitationsare overcome by utilizing the apparatus depicted in FIG. 2. As shown inFIG. 2, only one mixer 13 is used, therefore eliminating any errorsarising from unequal mixer gains. It will also be noted that an analogphase shift network is not required, thus eliminating impropermaintenance of quadrature as a source of error. The signal to bemeasured is applied via terminal 11 to mixer 13 wherein it issuccessively and periodically product modulated by four quadraturerelated waveforms, i.e., waveforms displaced in phase by 11/2 radians asdepicted in FIG. 3, each having a fundamental frequency equal to theapplied input signal. The modulating waveforms are applied by OR gate 33to mixer 13; the generation of these waveforms will be discussedhereinafter.

Considering only the fundamental frequency component of each pulse trainwaveform of FIG. 3, the modulating signals may be characterized by:

where n= 1= 2= a= Stated another way, S, lags S S lags S and S lags eachrespectively by precisely 1r/2 radians, i.e., After successivemodulation of the input signal, in mixer 13, with each waveform andfiltering, four successive output signals, Y, appear at the output oflow-pass filter 16, each corresponding to a modulation product of theinput signal and a waveform having the same identifying subscript, i.These signals may be ex- Y =GA sin 0+D. (6) It will be noted that thegain term G is identical for each signal, since the same mixer is used,and that the d.c. drift term D is also common to all signals. Eachsignal Y, is respectively applied via gates 34, 35, 36, and 37 to astorage network 42, 43, 44, 45. The output signals of the storagenetworks are combined by subtractors 39 and 41 to develop two signals 1and U which may be expressed as:

The drift term D of each signal Y, fortuitously cancels, and since thetwo signals are generated by the same product detector 13, the same gaincoefiicient G is present in each signal.

Furthermore, crosstalk, a recurring problem in prior art ysystems,betweenthe inphase and quadrature channel signals, 1 cannot 'occur sincethe successive modulations of the input signal are necessarily distinctin time. Accordingly, the limitations of prior art homodyne detectionapparatus, previously discussed, are overcome by the practice of thisinvention.

The two signals, 1 and U, are applied to computation apparatus 18,identical to that of FIG. 1, or any well-known equivalent, to developamplitude and phase proportional signals, respectively, at terminals 23and 26.

Turning now to the manner in which waveforms S, of FIG. 3

are generated, apparatus 61 of FIG. 2 comprises a clock 38straightforward application of well-known digital logic circuitprinciples, it may be readily shown that the desired waveforms A, I, B,and F appear at the terminals so designated. Each of these waveforms isapplied to a like designated terminal of gates 28, 29, 31, and 32.Simultaneously, synchronization, sync, generator 27 applies successiveenabling control signals 0,, 0,, Q and Q, to gates 28, 29, 31, and 32,and also to gates 34, 35, 36, and 37. Thus, when a signal is present, atthe Q terminal of generator 27, gate 28 is enabled and waveform Aapplied via OR gate 33 to mixer 13. Simultaneously, gate 34 is enabledby signal. 0., thereby allowing the product output signal of mixer 13and low-pass filter 16 to be applied to I storage network 42. In asimilar manner, the other waveforms B, A, and Eare consecutively appliedto mixer 13 by gates 29, 31, and 32, respectively, and the gates 35, 36,and 37 successively activated to apply the filtered product signals tostorage networks 43, 44, and 45. If the propagation delays of gates 28,29, 31, and 32 are unequal, a flip-flop circuit, response to timingsignals, T, may be inserted between OR gate 33 and mixer 13, to properlysynchronize the applied waveforms, S To allow 'sufficient time fortransients to decay, each of waveforms A, B, A and Bis applied to mixer13 for an interval of time equal to approximately 50 to 100 cycles ormore of the input signal, depending upon the particular filter 16 used.For example, in one embodiment of this invention, the frequency of theinput signal is equal to 278 KHz, and each waveform is applied to mixer13 and the resultant product signal to a storage network for an intervalof time equal to 250 microseconds. Of course, this interval of time maybe varied to suit the characteristics of a particular input signaland/or processing element. It is to be understood that the embodimentsshown and described herein are illustrative of the principles of thisinvention only, and that modifications of this invention may beimplemented by those skilled in the art without departing from the scopeand spirit of the invention; for example, the successive output signals,Y of filter 16 (FIG. 2) may be directly applied to a unitary holdingnetwork and then converted into digital form for subsequent processingby digital apparatus.

What is claimed is: 1. Improved homodyne detection apparatus responsiveto an applied signal comprising:

first means for generating a plurality of quadrature related signal,waveforms, each waveform having a frequency component corresponding tothe frequency of said applied signal; second means responsive to saidapplied signal and said signal waveforms for developing a plurality ofsuccessive product signals, each selectively proportional to the productof said applied signal and one of said signal waveforms; third means forstoring each of said product signals; and

fourth means for selectively combining said stored signals.

2. The apparatus defined in claim 1 wherein said second means includes aproduct modulator and a low-pass filter.

3. The apparatus defined in claim 2 wherein said second means furthercomprises:

a plurality of gate circuits, each gate circuit responsive to only oneof said plurality of signal waveforms;

means for successively enabling each of said gate circuits;

and

means for applying the output signals of said gate circuits to saidproduct modulator.

4. The apparatus of claim 1 wherein said plurality of signal waveformscomprises first, second, third, and fourth periodic pulse trains andwherein said second pulse train lags said first pulse train by 1r/2radians, said third pulse train lags said second pulse train by 11/2radians, and said fourth pulse train lags said third pulse train by M2radians.

5. An improved homodyne detector responsive to an applied input signalcomprising:

' first means for periodically generating a plurality of successivequadrature related periodic signal waveforms, each waveform having afundamental frequency equal to the frequency of said input signal;

second means responsive to said input signal and saidsuccessive'periodic signal wavefonns for developing a plurality ofproduct signals, each proportional to the product of said applied inputsignal and one of said signal waveforms;

third means for filtering said product signals;

fourth means for storing each of said filtered product signals; and

fifth means for selectively combining said stored signals.

6. The apparatus defined in claim 5 wherein said second means includes aproduct modulator.

7. The apparatus defined in claim 5 wherein said first means furthercomprises:

means for simultaneously generating a plurality of quadrature relatedperiodic signal waveforms;-

a plurality of gate circuits, each gate circuit responsive to only oneof said plurality of signal waveforms;

means for successively enabling each of said gate circuits;

and

means for applying the output signals of said gate circuits to saidsecond means.

8. The apparatus defined in claim 7 wherein said means for generatingsaid plurality of signal waveforms comprises:

first and second multivibrators each having first and second inputs andfirst and second outputs;-

a plurality of logic circuits, each logic circuit respectively connectedto one of said inputs of said first and second multivibrators; and

a source of timing signals connected to an input of each of said logiccircuits, the first output .of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator'firstinput, the second output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator secondinput, the first output of said first multivibrator connected to aninput of said logic circuit connected to said second multivibratorsecond input, and the second output of said first multivibratorconnected to an input of said logic circuit connected to said secondmultivibrator first input.

9. The apparatus of claim 5 wherein said plurality of signal waveformscomprises first, second, third, and fourth periodic pulse trains andwherein said second pulse train lags said first pulse train by 1r/2radians, said third pulse train lags'said second pulse train by 11/2radians, and said fourth pulse train lags said third pulse train by 1r/2radians.

10. An improved homodyne detector responsive to an applied input signalcomprising:

first means for periodically generating a plurality of successiveperiodic signal waveforms, each waveform having a fundamental frequencycorresponding to the frequency of said input signal and electricallydisplaced from a preceding waveform by a phase shift of 1r/2 radians;

second means responsive to said input signal and said successiveperiodic signal waveforms for developing a plurality of signals, eachproportional to the product of said input signal and one of said signalwaveforms;

third means for filtering said product signals;

fourth means for storing each of said filtered product signals; and

fifth means for arithmetically combining said stored signals.

11. An improved homodyne detector responsive to an applied input signalcomprising:

first means for generating a plurality of signal waveforms, eachwaveform having a fundamental frequency equal to the frequency of saidinput signal and shifted one from another by a phase shift of 1r/2radians; I

second means responsive to said input signal and an applied waveform fordeveloping a signal proportional to the product of said input signal andan applied waveform;

third means for successively applying said phase shifted waveforms tosaid second means;

fourth means for filtering each of the successively developed productsignals;

fifth means for storing each of said filtered product signals;

and

sixth means for arithmetically combining said stored signals.

12. The apparatus defined in claim 11 wherein said first meanscomprises:

first and second multivibrators each having first and second inputs andfirst and second outputs;

a plurality of logic circuits, each logic circuit respectively connectedto one of said inputs of said first and second multivibrators; and

a source of timing signals connected to an input of each of said logiccircuits, the first output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator firstinput, the second output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator secondinput, the first output of said first multivibrator connected to aninput of said logic circuit connected to said second multivibratorsecond input, and the second output of said first multivibratorconnected to an input of said logic circuit connected to said secondmultivibrator first input.

13. The apparatus defined in claim 11 wherein said third meanscomprises:

a plurality of gate circuits, each gate circuit responsive to only oneof said plurality of signal waveforms;

means for successively enabling each of said gate circuits;

and

means for applying the output signals of said gate circuits to saidsecond means.

14 The apparatus of claim 11 wherein said plurality of signal waveformscomprises first, second, third, and fourth periodic pulse trains andwherein said second pulse train lags said first pulse train by 1r/2radians, said third pulse train lags said second pulse train by 1r/2radians, and said fourth pulse train lags said third pulse train by 77/2radians.

l5. Amplitude and phase measuring apparatus responsive to an appliedsignal comprising:

first means for periodically generating a plurality of successive signalwaveforms, each waveform having a fundamental frequency equal to thefrequency of said applied signal and electrically displaced from animmediately preceding waveform by a phase shift of 1r/2 radians;

second means responsive to said applied signal and said successivewaveforms for successively developing a plurality of signals, eachproportional to the product of said applied signal and one of saidwavefonns;

third means for filtering each of said plurality of product signals;

fourth means for separately storing each of said filtered productsignals;

fifth means for selectively combining said stored signals to removeundesired error components; and

sixth means responsive to said combined signals for developing signalsproportional to the phase and amplitude of said applied signal.

16. The apparatus defined in claim 15 wherein said second means includesa mixer.

17. The apparatus defined in claim 16 wherein said first means furthercomprises:

means for generating said plurality of signal waveforms;

a plurality of gate circuits, each gate circuit responsive to only oneof said plurality of signal waveforms;

means for successively enabling each of said gate circuits;

and

means for applying the output signals of said gate circuits to saidmixer.

18. The apparatus defined in claim 17 wherein said means for generatingcomprises:

first and second multivibrators each having first and second inputs andfirst and second outputs;

a plurality of logic circuits, each logic circuit respectively connectedto one of said inputs of said first and second multivibrators; and

a source of timing signals connected to an input of each of said logiccircuits, the first output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator firstinput, the second output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator secondinput, the first output of said first multivibrator connected to aninput of said logic circuit connected to said second multivibratorsecond input, and the second output of said first multivibratorconnected to an input of said logic circuit connected to said secondmultivibrator first input.

19. The apparatus of claim 18 wherein said plurality of signal waveformscomprises first, second, third, and fourth periodic pulse trains andwherein said second pulse train lags said first pulse train by 1r/2radians, said third pulse train lags said second pulse train by 11/2radians, and said fourth pulse train lags said third pulse train by 11/2radians.

1. Improved homodyne detection apparatus responsive to an applied signalcomprising: first means for generating a plurality of quadrature relatedsignal waveforms, each waveform having a frequency componentcorresponding to the frequency of said applied signal; second meansresponsive to said applied signal and said signal waveforms fordeveloping a plurality of successive product signals, each selectivelyproportional to the product of said applied signal and one of saidsignal waveforms; third means for storing each of said product signals;and fourth means for selectively combining said stored signals.
 2. Theapparatus defined in claim 1 wherein said second means includes aproduct modulator and a low-pass filter.
 3. The apparatus defined inclaim 2 wherein said second means further comprises: a plurality of gatecircuits, each gate circuit responsive to only one of said plurality ofsignal waveforms; means for successively enabling each of said gatecircuits; and means for applying the output signals of said gatecircuits to said product modulator.
 4. The apparatus of claim 1 whereinsaid plurality of signal waveforms comprises first, second, third, andfourth periodic pulse trains and wherein said second pulse train lagssaid first pulse train by pi /2 radians, said third pulse train lagssaid second pulse train by pi /2 radians, and said fourth pulse trainlags said third pulse train by pi /2 radians.
 5. An improved homodynedetector responsive to an applied input signal comprising: first meansfor periodically generating a plurality of successive quadrature relatedperiodic signal waveforms, each waveform having a fundamental frequencyequal to the frequency of said input signal; second means responsive tosaid input signal and said successive periodic signal waveforms fordeveloping a plurality of product signals, each proportional to theproduct of said applied input signal and one of said signal waveforms;third means for filtering said product signals; fourth means for storingeach of said filtered product signals; and fifth means for selectivelycombining said stored signals.
 6. The apparatus defined in claim 5wherein said second means includes a product modulator.
 7. The apparatusdefined in claim 5 wherein said first means further comprises: means forsimultaneously generating a plurality of quadrature related periodicsignal waveforms; a plurality of gate circuits, each gate circuitresponsive to only one of said plurality of signal waveforms; means forsuccessively enabling each of said gate circuits; and means for applyingthe output signals of said gate circuits to said second means.
 8. Theapparatus defined in claim 7 wherein said means for generating saidplurality of signal waveforms comprises: first and second multivibratorseach having first and second inputs and first and second outputs; aplurality of logic circuits, each logic circuit respectively connectedto one of said inputs of said first and second multivibrators; and asource of timing signals connected to an input of each of said logiccircuits, the first output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator firstinput, the second output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator secondinput, the first output of said first multivibrator connected to aninput of said logic circuit connected to said second multivibratorsecond input, and the second output of said first multivibratorconnected to an input of said logic circuit connected to said secondmultivibrator first input.
 9. The apparatus of claim 5 wherein saidplurality of signal waveforms comprises first, second, third, and fourthperiodic pulse trains and wherein said second pulse train lags saidfirst pulse train by pi /2 radians, said third pulse train lags saidsecond pulse train by pi /2 radians, and said fourth pulse train lagssaid third pulse train by pi /2 radians.
 10. An improved homodynedetector responsive to an applied input signal comprising: first meansfor periodically generating a plurality of successive periodic signalwaveforms, each waveform having a fundamental frequency corresponding tothe frequency of said input signal and electrically displaced from apreceding waveform by a phase shift of pi /2 radians; second meansresponsive to said input signal and said successive periodic signalwaveforms for developing a plurality of signals, each proportional tothe product of said input signal and one of said signal waveforms; thirdmeans for filtering said product signals; fourth means for storing eachof said filtered product signals; and fifth means for arithmeticallycombining said stored signals.
 11. An improved homodyne detectorresponsive to an applied input signal comprising: first means forgenerating a plurality of signal waveforms, each waveform having afundamental frequency equal to the frequency of said input signal andshifted one from another by a phase shift of pi /2 radians; second meansresponsive to said input signal and an applied waveform for developing asignal proportional to the product of said input signal and an appliedwaveform; third means for successively applying said phase shiftedwaveforms to said second means; fourth means for filtering each of thesuccessively developed product signals; fifth means for storing each ofsaid filtered product signals; and sixth means for arithmeticallycombining said stored signals.
 12. The apparatus defined in claim 11wherein said first means comprises: first and second multivibrators eachhaving first and second inputs and first and second outputs; a pluraLityof logic circuits, each logic circuit respectively connected to one ofsaid inputs of said first and second multivibrators; and a source oftiming signals connected to an input of each of said logic circuits, thefirst output of said second multivibrator connected to an input of saidlogic circuit connected to said first multivibrator first input, thesecond output of said second multivibrator connected to an input of saidlogic circuit connected to said first multivibrator second input, thefirst output of said first multivibrator connected to an input of saidlogic circuit connected to said second multivibrator second input, andthe second output of said first multivibrator connected to an input ofsaid logic circuit connected to said second multivibrator first input.13. The apparatus defined in claim 11 wherein said third meanscomprises: a plurality of gate circuits, each gate circuit responsive toonly one of said plurality of signal waveforms; means for successivelyenabling each of said gate circuits; and means for applying the outputsignals of said gate circuits to said second means.
 14. The apparatus ofclaim 11 wherein said plurality of signal waveforms comprises first,second, third, and fourth periodic pulse trains and wherein said secondpulse train lags said first pulse train by pi /2 radians, said thirdpulse train lags said second pulse train by pi /2 radians, and saidfourth pulse train lags said third pulse train by pi /2 radians. 15.Amplitude and phase measuring apparatus responsive to an applied signalcomprising: first means for periodically generating a plurality ofsuccessive signal waveforms, each waveform having a fundamentalfrequency equal to the frequency of said applied signal and electricallydisplaced from an immediately preceding waveform by a phase shift of pi/2 radians; second means responsive to said applied signal and saidsuccessive waveforms for successively developing a plurality of signals,each proportional to the product of said applied signal and one of saidwaveforms; third means for filtering each of said plurality of productsignals; fourth means for separately storing each of said filteredproduct signals; fifth means for selectively combining said storedsignals to remove undesired error components; and sixth means responsiveto said combined signals for developing signals proportional to thephase and amplitude of said applied signal.
 16. The apparatus defined inclaim 15 wherein said second means includes a mixer.
 17. The apparatusdefined in claim 16 wherein said first means further comprises: meansfor generating said plurality of signal waveforms; a plurality of gatecircuits, each gate circuit responsive to only one of said plurality ofsignal waveforms; means for successively enabling each of said gatecircuits; and means for applying the output signals of said gatecircuits to said mixer.
 18. The apparatus defined in claim 17 whereinsaid means for generating comprises: first and second multivibratorseach having first and second inputs and first and second outputs; aplurality of logic circuits, each logic circuit respectively connectedto one of said inputs of said first and second multivibrators; and asource of timing signals connected to an input of each of said logiccircuits, the first output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator firstinput, the second output of said second multivibrator connected to aninput of said logic circuit connected to said first multivibrator secondinput, the first output of said first multivibrator connected to aninput of said logic circuit connected to said second multivibratorsecond input, and the second output of said first multivibratorconnected to an input of said logic circuit connected to said secondmultivibrator first input.
 19. The apparatus of claim 18 whereiN saidplurality of signal waveforms comprises first, second, third, and fourthperiodic pulse trains and wherein said second pulse train lags saidfirst pulse train by pi /2 radians, said third pulse train lags saidsecond pulse train by pi /2 radians, and said fourth pulse train lagssaid third pulse train by pi /2 radians.